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As part of a program to study odd-A nuclei in the Hartree-Fock-Bogoliubov(HFB) theory, we have developed a new calculational tool to find the HFB minimaof odd-A nuclei based on the gradient method and using interactions of Gogny'sform. The HFB minimization includes both time-even and time-odd fields in theenergy functional, avoiding the commonly used "filling approximation". Here weapply the method to calculate neutron pairing gaps in some representativeisotope chains of spherical and deformed nuclei, namely the Z=8,50 and 82spherical chains and the Z=62 and 92 deformed chains. We find that the gradientmethod is quite robust, permitting us to carry out systematic surveys involvingmany nuclei. We find that the time-odd field does not have large effect on thepairing gaps calculated with the Gogny D1S interaction. Typically, adding theT-odd field as a perturbation increases the pairing gap by ~100 keV, but there-minimization brings the gap back down. This outcome is very similar toresults reported for the Skyrme family of nuclear energy density functionals.Comparing the calculated gaps with the experimental ones, we find that thetheoretical errors have both signs implying that the D1S interaction has areasonable overall strength. However, we find some systematic deficienciescomparing spherical and deformed chains and comparing the lighter chains withthe heavier ones. The gaps for heavy spherical nuclei are too high, while thosefor deformed nuclei tend to be too low. The calculated gaps of spherical nucleishow hardly any A-dependence, contrary to the data. Inclusion of the T-oddcomponent of the interaction does not change these qualitative findings.

Pairing gaps in Hartree-Fock Bogoliubov theory with the Gogny D1S interaction